Question
Determine the limit of the sequence or show that the sequence diverges. If it converges, find its limit.$$a_{n}=(2 n)^{1 / n}-n^{1 / n}$$
Step 1
Step 1: First, we can rewrite the given sequence as follows: $$a_{n}=n^{1 / n}(2^{1 / n}-1)$$ This is achieved by factoring out $n^{1 / n}$ from the original sequence. Show more…
Show all steps
Your feedback will help us improve your experience
Linh Vu and 79 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Determine the limit of the sequence or show that the sequence diverges. If it converges, find its limit. $$a_{n}=\left(1-\frac{2}{n}\right)^{n}$$
Sequences and Series
Sequences
Determine the limit of the sequence or show that the sequence diverges. If it converges, find its limit. $$a_{n}=\frac{(n !)^{2}}{(2 n) !}$$
Determine the limit of the sequence or show that the sequence diverges. If it converges, find its limit. $$a_{n}=\frac{\ln \left(n^{2}\right)}{\ln (2 n)}$$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD